The GCF of the two expressions is (y + 5).
How can we prove it ?The greatest common factor (GCF) of two or more expressions is the largest expression that is a factor of each of the expressions. To find the GCF of two expressions, we need to factor out the common factors from each expression.
Given expressions: z(y + 5) - 3(y + 5)
We can start by factoring out (y + 5) from both terms:
z(y + 5) - 3(y + 5) = (y + 5)(z - 3)
So, the GCF of the two expressions is (y + 5).
What is GCF?The greatest common factor (GCF) is the largest positive integer that is a factor of two or more numbers. It is a useful concept in mathematics, especially in the study of numbers and their properties. The GCF helps us simplify expressions by cancelling out common factors and reducing the complexity of expressions. For example, the GCF of 12 and 18 is 6, meaning that 6 is the largest number that is a factor of both 12 and 18. To find the GCF, we can use prime factorization to identify the common factors and then multiply those factors to obtain the GCF.
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At a plant, 30% of all the produced parts are subject to a special electronic inspection. It is known that any produced part which was inspected electronically has no defects with probability 0.90. For a part that was not inspected electronically this probability is only 0.80 Let E be the event that a part in the plant went through an electronic inspection Let D be the event that a part produced in the plant is defective. Find the following A- P(E) B- P (DE) C- P(DE) D- P(DE) A- P(E) B. P (DE) CP (DE) D- P (DE) E- P(DE) F- P(D) G- P(ED) TYPE YOUR FINAL ANSWERS. LABEL YOUR ANSWERS AS A, B
30% of parts undergo electronic inspection. If inspected, the chance of no defects is 90%. If not inspected, chance of defects is 20%. Total chance of a defect is 27%. Chance of a defective part being inspected is 33%.
A. P(E) = 0.30, the probability that a part in the plant went through an electronic inspection.
B. P(D|E) = 0.90, the probability that a produced part which was inspected electronically has no defects.
C. P(D|E') = 0.20, the probability that a part produced in the plant is defective and was not inspected electronically.
D. P(E') = 0.70, the probability that a part in the plant did not go through an electronic inspection.
E. P(D|E) + P(D|E') = 0.90 + 0.20 = 1.10, which is not a valid probability value since it is greater than 1.
F. P(D) = P(D|E)P(E) + P(D|E')P(E') = 0.90 * 0.30 + 0.20 * 0.70 = 0.27, the probability that a part produced in the plant is defective.
G. P(E|D) = P(DE) / P(D) = 0.90 * 0.30 / 0.27 = 0.33, the probability that a defective part in the plant went through an electronic inspection.
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motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. assume a production process produces items with a mean weight of
The normal distribution is a probability distribution used to describe the probability of a given value of a continuous variable.
The normal distribution is characterized by two parameters, the mean and standard deviation. The mean, μ, represents the center of the distribution, and the standard deviation, σ, represents the spread of the distribution.
In a production process, the normal distribution can be used to predict the probability of defects and the number of defects expected for a given mean and standard deviation. The probability of a given defect can be calculated using the formula p = 1-N(x; μ, σ), where N(x; μ, σ) is the cumulative normal distribution function, x is the number of defects, μ is the mean, and σ is the standard deviation.
For example, if a production process produces items with a mean weight of 10 grams and a standard deviation of 1 gram, then the probability of a defect occurring is calculated using the formula: p = 1-N(x; 10, 1). If we assume a defect occurs at 8 grams, then the probability of a defect occurring is 1-N(8; 10, 1) = 0.1587. This means that there is a 15.87% chance of a defect occurring in the production process.
To calculate the expected number of defects, we can use the formula E(x) = μ + (σ * N’(p)), where N’(p) is the inverse normal distribution function and p is the probability of a defect occurring. Using the example above, we can calculate the expected number of defects as 10 + (1 * N’(0.1587)) = 10.24, meaning that we can expect 10.24 defects for every 100 items produced.
In this example, there is a 15.87% chance of a defect occurring in the production process, and we can expect 10.24 defects for every 100 items produced.
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Find the next three terms
-8, -12, -18, -27
The next three terms of the sequence are - 40.5, - 60.75 , -91.125
What is geometric sequence?A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
The nth term of a geometric sequence is given as a(n) = ar^n-1
where a is the first term and r is the common ratio
to find the common ratio:
r = a2/a1
r = -12/-8
r = 1.5
-27 is the fourth term = ar³
fifth term = ar³× r
= -27 × 1.5 = -40.5
sixth term = -40.5 × 1.5 =- 60.75
seventh term = -60.75 × 1.5 = -91.125
therefore the next three terms of the sequence are - 40.5, - 60.75 , -91.125
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HELP!!!Joe can type 40 words every 2 minutes. How many words can he type in 5 minutes?
Answer:100
Step-by-step explanation:
40+40 =80 +20=100
fill in the blank.when we have a___data set it is like the scrambled phrase. statistic is the process of using visual, numerical, and tabular display to unscramble the data and discover the message behind it
When we have a population data set it is like the scrambled phrase. statistic is the process of using visual, numerical, and tabular display to unscramble the data and discover the message behind it.
A collection of data is known as a data set (or dataset). In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable. The data set includes values for each of the variables, such as the object's height and weight, for each set member. Data sets can also be made up of a group of files or documents.
The analysis and manipulation of data is the essence of statistics. As we just covered in the introduction, statistics is the study of the calculation and analysis of numerical data. Let's examine other statistical definitions provided by various authors in this article.
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Use the disk method or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line x2 (a) the x-axis (b) the y-axis (c) the line x = 5 Need Help? Read ItTalk to a Tutor +-4 points LarCalc11 7.3.030.MI. Use the disk method or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line 10 x2 (a) the x-axis (b) the y-axis (c) the line y 10
Using either shell method, the volume of the solid generated by revolving the region bounded by y = [tex]x^{3}[/tex] and y = 0 around the lines x = 2 (a), x = 0 (b), and x = 9 (c) can be determined to be 8π, 0, and 54π, respectively.
To solve this problem using the disk method, we first need to determine the area of the region bounded by the two equations. This can be done by integrating y = [tex]x^{3}[/tex] from x = 0 to x = 2, which gives us A = 8/4 = 2. We then need to determine the radius of the disk, which is the distance from the line of rotation to the point of intersection of the two equations.
For (a), this is the distance from x = 2 to y = 2, which is 2. For (b), this is the distance from x = 0 to y = 0, which is 0. For (c), this is the distance from x = 9 to y = 27, which is 27/3. We can now use the formula for the volume of a solid generated by revolving a region around a line to calculate the volume for each of the three lines:
(a) V = π(2)2 × 2 = 8π
(b) V = π(0)2 × 2 = 0
(c) V = π(27/3)2 × 2 = 54π
To solve this problem using the shell method, we first need to determine the limits of integration, which is the same as for the disk method. We then need to determine the radius of the shell, which is the distance from the line of rotation to the point of intersection of the two equations.
This is the same as for the disk method. We can now use the formula for the volume of a solid generated by revolving a region around a line to calculate the volume for each of the three lines:
(a) V = 2π ∫(2) ([tex]x^{3}[/tex]) dx = 8π
(b) V = 2π ∫(0) ([tex]x^{3}[/tex]) dx = 0
(c) V = 2π ∫(27/3) ([tex]x^{3}[/tex]) dx = 54π
The disk and shell methods are two methods used to find the volume of a solid generated by revolving a region bounded by the graphs of two equations around a given line.
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fill in the blank. consider a sample with a mean of and a standard deviation of ___. use chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number).
100% of the data lies within two standard deviations of the mean, 75% of the data lies within one standard deviation of the mean, and 50% of the data lies between 8 and 12.
Consider a sample with a mean of 10 and a standard deviation of 4. Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number):
- Between 2 and 18: 100%
- Between 6 and 14: 75%
- Between 8 and 12: 50%
Chebyshev's theorem states that at least 75% of the data will lie within two standard deviations of the mean, and at least 50% of the data will lie within one standard deviation of the mean. In this example, 100% of the data lies within two standard deviations of the mean, 75% of the data lies within one standard deviation of the mean, and 50% of the data lies between 8 and 12.
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A bicycle is traveling at 19 miles per hour.
How many feet will it cover in 30 seconds?
Round your answer to the nearest tenth of a foot.
The distance covered by the bicycle is 0.2 miles.
How to find the distance covered?A bicycle is traveling at 19 miles per hour. The number of feet the bicycle will cover in 30 seconds can be calculated as follows:
Therefore,
speed = distance / time
Hence, let's find the distance covered by the bicycle using the data given:
speed = 19 miles per hour
time = 30 seconds = 0.00833333 hours
Therefore,
distance covered = speed × time
distance covered = 19 × 0.00833333
distance covered = 0.15833327
distance covered = 0.2 miles
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Principal and interest are always
Answer:
amounts of
Step-by-step explanation:
In a principal + interest loan, the principal (original amount borrowed) is divided into equal monthly amounts, and the interest (fee charged for borrowing) is calculated on the outstanding principal balance each month.
Hope this helps!
Halla el FCM de 126, 119 y 196 usando el método de factorización prima
The HCF of the numbers 126, 119 and 196 is 7.
What is HCF?The Highest Common Factor (HCF) of two numbers is the highest possible number that divides both the numbers completely.
The Highest Common Factor (HCF) is also called the Greatest Common Divisor (GCD).
Given are the numbers -
126, 119, 196
We can write the Prime factorization of the numbers given as -
126 = 2 × 3 × 3 × 7
119 = 7 × 17
196 = 2 × 2 × 7 × 7
7 is common in the prime factorization of all the numbers.
Therefore, the HCF of the numbers 126, 119 and 196 is 7.
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{
Complete question in english -
Find the FCF of 126, 119, and 196 using the prime factorization method
}
3. suppose you are given two circularly linked lists, l and m. describe an algorithm for telling if l and m store the same sequence of elements (but perhaps with different starting points).
The logic for the algorithm is Traverse both linked lists, comparing corresponding elements.
To determine if two circular linked lists, l and m, store the same sequence of elements, we can use the following algorithm:
Start at the head of both linked lists, l and m, and traverse each list until we reach the end.At each step, compare the elements stored in the corresponding nodes of both linked lists.If the elements are not equal, the lists do not store the same sequence of elements.If we reach the end of both linked lists and all elements have been equal, the lists store the same sequence of elements, but with different starting points.In order to cover the case where the lists store the same sequence of elements but with different starting points, we can repeat the algorithm starting at each node in l and m, and continue until we have compared all possible starting points.Learn more about linked lists:
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subtract y from 5, then double the result
The expression of the given algebra word problem is; 10 - 2y
How to simplify algebraic expressions?We are told that we should subtract y from 5, then double the result.
Subtracting y from 5 gives us;
5 - y
Now, doubling the result will mean we will multiply it by 2 and this will be expressed as;
2(5 - y)
Expanding the bracket using distributive property is;
2*5 - 2*y
= 10 - 2y
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Solve the equation:
6x³+24x²+24x=0
x=0 and x=-2 are the solutions of the equation 6x³+24x²+24x=0
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given equation is 6x³+24x²+24x=0
Take 6x as common from the given equation.
6x(x²+4x+4)=0
6x=0 and x²+4x+4=0
x²+4x+4=0
x²+2x+2x+4=0
x(x+2)+2(x+2)=0
(x+2)(x+2)=0
(x+2)²=0
x=-2
Hence, x=0 and x=-2 are the solutions of the equation 6x³+24x²+24x=0
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Suppose that there was a cancer diagnostic test that was 95% accurate both on those that do and those that do not have the disease. If 40 percent of the population has cancer, compute the probability that a tested person has cancer, given that their test result indicates so.
The conditional probability that a tested person has cancer, given that their test result indicates so, is given as follows:
0.9268 = 92.68%.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering the result of a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of the event B happening, given that the event A happened.[tex]P(A \cap B)[/tex] is the probability of both the events A and B happening.P(A) is the probability of the event A happening.The events for this problem are given as folows:
Event A: positive test result.Event B: person has cancer.The probability of a positive test result are given as follows:
95% of 40% -> has cancer.5% of 60% -> does not have cancer.Hence:
P(A) = 0.95 x 0.4 + 0.05 x 0.6 = 0.41.
Hence the conditional probability is given as follows:
P(B|A) = 0.95 x 0.4/0.41 = 0.9268 = 92.68%.
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Enter an equation in the form y=mx+b that represents the function defined by this table of values.
The linear function that represents the table values is y = 3x + 5.
What is the linear function that represents the table values?
The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Using two points from the table, (0,5) and (2,11)
First, we determine the slope m.
Slope m = change in y / change in x
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Plug in the values
Slope m = ( 11 - 5 ) / ( 2 - 0 )
Slope m = 6 / 2
Slope m = 3
Plug the slope m =3 and point (0,5) into the point-slope formula and simplify.
y - y₁ = m( x - x₁ )
y - 5 = 3( x - 0 )
y - 5 = 3x - 0
y - 5 = 3x
Add 5 to both sides
y - 5 + 5 = 3x + 5
y = 3x + 5.
Therefore, the equation of the line is y = 3x + 5.
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i) Group 1 contains 170 students, all of whom have taken at least one of the three courses listed above. Of these, 61 students have taken Calculus, 78 have taken Sociology, and 72 have taken Spanish. 15 have taken both Cal- culus and Sociology, 20 have taken both Calculus and Spanish, and 13 have taken both Sociology and Spanish. How many students have taken all three classes? (ii) You are given the following data about Group 2. 32 students have taken Calculus, 22 have taken Sociology, and 16 have taken Spanish. 10 have taken both Calculus and Sociology, 8 have taken both Calculus and Span- ish, and 11 have taken both Sociology and Spanish. 5 students have taken all three courses while 15 students have taken none of the courses. How many students are in Group 2?
The number of students that took all the three classes is 40
The number of students are in Group 2 is 51 students
How to find the number of students that tool all the three classes(i) To find the number of students who have taken all three classes, we need to subtract the number of students who have taken only two classes from the number of students who have taken at least one class.
Let's call the number of students who have taken all three classes "x".
The number of students who have taken Calculus and Sociology is 15 + x.
The number of students who have taken Calculus and Spanish is 20 + x.
The number of students who have taken Sociology and Spanish is 13 + x.
Adding these three equations, we have:
15 + 78 + 72 = 15 + x + 78 + x + 72 + x
solving for x
165 = 45 + 3x
120 = 3x
isolating x
So, x = 40.
hence, 40 students have taken all three classes.
(ii) To find the number of students in Group 2, we need to add the number of students who have taken at least one class to the number of students who have taken none of the classes.
Let's call the number of students in Group 2 "y".
The number of students who have taken at least one class is
32 + 22 + 16 - 10 - 8 - 11 + 5 = 36.
Therefore, y = 36 + 15 = 51.
So, there are 51 students in Group 2.
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the empirical rule provides precise statements regarding the percentage of observations that fall within a specified number of standard deviations from the mean. which of the following is a correct statement? select all that apply!
The correct answer is option A. The empirical rule provides precise statements regarding 1, 2, or 3 standard deviations.
The Empirical Rule, also known as the 68-95-99.7 rule, states that for a normal distribution (or approximately normal distribution), about 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This rule assumes that the mean, median, and mode are equal and the data is symmetrical.
It is a quick and easy way to get a rough estimate of the spread of data in a normal distribution and the proportion of values that fall within certain intervals. However, it should be noted that this is an approximation and not always accurate, especially for distributions that are not close to being normal.
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Complete Question:
When applicable, the empirical rule provides the approximate percentage of observations that fall within how many standard deviations from the mean?
A. 1, 2, or 3 standard deviations
B. 4, 6, or 9 standard deviations
C. 2, 2, or 7 standard deviations
A psychology professor wants to know whether verbal ability is related to memory quality in current first-year students at his small college. Participants in the study (first-year students at his college) complete an online memory task. The students are first shown a list of 60 words. Next they are shown a list that includes 10 words that were on the original list. Then they are asked to identify the words on the second list that appeared on the original list. He uses the percentage of words that were correctly recognized on the original list as his measure of memory quality. He also asks the students to report several characteristics such as their age, gender, and verbal SAT score. Each of the 500 first-year students (268 males and 232 females) at his school volunteered to participate. The professor chose 50 students at random to complete the memory task and answer the questions. The average percentage of words that were correctly recognized on the original list was 68%. The professor infers that if all 500 first-year students had completed the study, the results would show that an average of 68% (plus or minus sampling error) of the words were correctly recognized as being on the original list. Which of the following are variables in the study? Check all that apply. The 500 students The students' percentage of words that were correctly recognized on the original list The students' verbal SAT scores The 50 students What is the population in the study? The 500 first-year students at the college The 68% of words correctly recognized as being on the original list The 50 students who participated in the study What is the sample in the study? The 50 students who participated in the study The 500 student volunteers The 68% of words correctly recognized as being on the original list What is an example of a statistic in the study? 68%, the average percentage of the original list expected to be correctly recognized by the 500 students 232 females and 268 males 68%, the average percentage of words that were correctly recognized as being from the original list by the 50 students What is an example of a parameter in the study? 68% of words that were correctly recognized on the original list by the 50 first-year students The actual average percentage of words that would be correctly recognized as being from the original list by the 500 first-year students 50 students What is an example of the professor using descriptive statistics? He characterizes the first-year students at the college as consisting of 268 males and 232 females. He randomly chooses the 50 students to represent the 500 volunteers. He infers that if all 500 students had done the experiment, the results would show that an average of 68% (plus or minus sampling error) of the words were correctly recognized as being on the original list. What is an example of the professor using inferential statistics? He infers that if all 500 students had done the experiment, the results would show that an average of 68% (plus or minus sampling error) of the words were correctly recognized as being on the original list. He characterizes the first-year students at the college as consisting of 268 males and 232 females. He reports that the average percentage of words that were correctly recognized on the original list was 68%.
Answer:
A
Step-by-step explanation:
y=-3x+2 determine the value of y when x=2
Answer:
[tex]\huge\boxed{\sf y = -4}[/tex]
Step-by-step explanation:
Given equation:y = -3x + 2
Given that, x = 2
So,
y = -3(2) + 2
y = -6 + 2
y = -4
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
replace where x is with 2
[tex]y = ( - 3 \times 2) + 2[/tex]
[tex]y = - 6 + 2[/tex]
Answer[tex]y = - 4[/tex]
Refer to the Figure given below. Without trade, Arturo produced and consumed 240 tacos and 120 burritos and Dina produced and consumed 100 tacos and 150 burritos. Then, each person agreed to specialize in the production to the good in which they have a comparative advantage and trade 260 tacos for 156 burritos. as a result, Arturo gains:a. 20 tacos and 24 burritos and Dina gained 40 tacos and 6 burritos,b. 20 tacos and 36 burritos and Dina gained 160 tacos and 6 burritos,c. 260 tacos and 144 burritos and Dina gained 140 tacos and 156 burritos,d. 260 tacos and 156 burritos and Dina gained 260 tacos and 156 burritos.
The correct answer is d. 260 tacos and 156 burritos and Dina gained 260 tacos and 156 burritos.
If each person specializes in the production of the good in which they have a comparative advantage and trade 260 tacos for 156 burritos, this means that both individuals benefit from trade as they can consume more of both goods than they would have without trade. Arturo specializes in producing tacos, which he trades for burritos produced by Dina. Similarly, Dina specializes in producing burritos, which she trades for tacos produced by Arturo. As a result, both individuals gain from trade, and the combined total of tacos and burritos remains the same after trade as before. In this case, both Arturo and Dina would end up with 260 tacos and 156 burritos each, which is the outcome of trade.
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please help with question
The solution is Option A.
The value of the equation is g ( x - 3 ) = √ ( x - 12 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as g ( x )
Now , the value of g ( x ) is
Substituting the values in the equation , we get
g ( x ) = √ ( x - 9 ) be equation (1)
On simplifying the equation , we get
when the value of x is x - 3 , we get
g ( x - 3 ) = √ ( x - 3 ) - 9
On further simplification , we get
g ( x - 3 ) = √ ( x - 3 - 9 )
g ( x - 3 ) = √ ( x - 12 )
Hence , the equation is g ( x - 3 ) = √ ( x - 12 )
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Tyrell is traveling to Chicago, Illinois. He takes a cab service from the airport to his hotel. The table shows the linear relationship between the number of miles the cab travels, x, and the total fee, y.
Cab Fare
Number of Miles Total Fee
2 $17.00
5 $21.50
7 $24.50
10 $29.00
15 $36.50
What does the y-intercept mean in this situation?
When the cab travels 0 miles, the total fee will be $14.00.
When the cab travels 0 miles, the total fee will be $1.50.
For every additional mile the cab travels, the total fee increases by $14.00.
For every additional mile the cab travels, the total fee increases by $1.50.
Answer:
The y-intercept in this situation means that when the cab travels 0 miles, the total fee will be $14.00. This indicates that the cab service charges a flat fee of $14.00, regardless of the number of miles traveled.
Step-by-step explanation:
The y-intercept in this situation represents the base fee that the cab service charges regardless of distance traveled. In this case, when the cab travels 0 miles, the total fee is $14.00.
Explanation:In this context, the y-intercept represents the base fee that the cab service charges, regardless of distance traveled. This is the amount you would pay for a cab ride of 0 miles. From the given table, we can't directly see the y-intercept, but we can infer it using the rate of change or slope, which represents the fee per mile. The amount increases by $1.50 for every additional mile (difference in y divided by difference in x), so to find the y-intercept, we back-calculate from one of the given points, like (2, 17). Subtracting 2 miles' worth of fees from $17 gives a y-intercept of $14. Therefore, when the cab travels 0 miles, the total fee is $14.00, which likely represents a starting charge or a minimum fare.
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Find the distance and the midpoints between each of the following given pairs of points. a) (0, 5) and (0 -6) b) (3, 0) and (-4, 0) c) (5, 2) and (7, 6) d) (-3, 4) and (1, -3) e) (6, 4) and (2, 1) f) (-2, -4) and (3, 8) g) (0, 0) and (5, 10) h) (2, 1) and (4, 0) i) (6, 4) and (6, -2) j) (-5, 2) and (7, -7)
a) Distance between given points = 11 unit ; Midpoint is (0 , -1/2)
b) Distance between given points = 7 unit ; Midpoint is (-1/2 , 0)
c) Distance between given points = 4.47 unit ; Midpoint is (6 , 4)
d) Distance between given points = 8.06 unit ; Midpoint is (-1 , 1/2)
e) Distance between given points = 5 unit ; Midpoint is (4 , 5/2)
f) Distance between given points = 13 unit ; Midpoint is (1/2 , 2)
g) Distance between given points = 5√5 unit ; Midpoint is (5/2 , 5)
h) Distance between given points = √5 unit ; Midpoint is (3 , 1/2)
i) Distance between given points = 6 unit ; Midpoint is (6 , 1)
j) Distance between given points = 15 unit ; Midpoint is (1 , -5/2)
What is the distance between two points?Distance between two points with coordinates (x₁ , y₁) and (x₂ , y₂). is given by
D = √[(x₁ - x₂)² + (y₁ - y₂)²]
This formula is derived from the Pythagoras Theorem, as the points form a right triangle in plane, with the hypotenuse representing the distance between them.
Given,
a) (0, 5) and (0 -6)
Distance = √[(0 - 0)² + (5 - -6)²] = √11² = 11 unit
Midpoint = [(x₁ + x₂)/2 + (y₁ + y₂)/2]
= [(0+0)/2 , (5 + -6)/2]
⇒ Midpoint = (0, -1/2)
b) (3, 0) and (-4, 0)
Distance = √[(3 - -4)² + (0 - 0)²] = √7² = 7 unit
Midpoint = [(x₁ + x₂)/2 + (y₁ + y₂)/2]
= [(3+ -4)/2 , (0 + 0)/2]
⇒ Midpoint = (-1/2, 0)
Similarly,
c) (5, 2) and (7, 6)
Distance = 4.47 unit
Midpoint = (6 , 4)
d) (-3, 4) and (1, -3)
Distance = 8.06 unit
Midpoint = (-1 , 1/2)
e) (6, 4) and (2, 1)
Distance = 5 unit
Midpoint = (4 , 5/2)
f)(-2, -4) and (3, 8)
Distance = 13 unit
Midpoint = (1/2 , 2)
g) (0, 0) and (5, 10)
Distance = 5√5 unit
Midpoint = (5/2 , 5)
h) (2, 1) and (4, 0)
Distance = √5 unit
Midpoint = (3 , 1/2)
i) (6, 4) and (6, -2)
Distance = 6 unit
Midpoint = (6 , 1)
j) (-5, 2) and (7, -7)
Distance = 15 unit
Midpoint = (1 , -5/2)
Hence,
a) Distance between points is 11 unit ; Midpoint = (0 , -1/2)
b) Distance between points is 7 unit ; Midpoint = (-1/2 , 0)
c) Distance between points is 4.47 unit ; Midpoint = (6 , 4)
d) Distance between points is 8.06 unit ; Midpoint = (-1 , 1/2)
e) Distance between points is 5 unit ; Midpoint = (4 , 5/2)
f) Distance between points is 13 unit ; Midpoint = (1/2 , 2)
g) Distance between points is 5√5 unit ; Midpoint = (5/2 , 5)
h) Distance between points is √5 unit ; Midpoint = (3 , 1/2)
i) Distance between points is 6 unit ; Midpoint = (6 , 1)
j) Distance between points is 15 unit ; Midpoint = (1 , -5/2)
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in lecture we showed that the closed-loop transfer function from the reference r(s) to the output y (s) for the unity feedback loop takes the form
This transfer function is a ratio between the gain of the controller (K) and the plant’s open-loop transfer function (G). The denominator is the sum of the gain and the plant’s transfer function, which results in the closed-loop feedback loop.
The closed-loop transfer function from the reference r(s) to the output y(s) for a unity feedback loop is given by:
y(s) = (K*G(s))/(1+K*G(s))
Where K is the gain of the controller, and G(s) is the plant’s open-loop transfer function. This can be derived by examining the block diagram of a unity feedback loop:
The input (r) is fed into a controller (K) whose output is then multiplied by the plant’s open-loop transfer function (G). The sum of the controller output and the plant output is then fed into the summing junction, and the output (y) is the result.
Therefore, the closed-loop transfer function representing the reference r(s) to the output y(s) can be derived as follows:
[tex]y(s) = r(s)*(K*G(s))/(1+K*G(s))\\= (K*G(s))/(1+K*G(s))[/tex]
This can be rearranged to give the final expression:
[tex]y(s) = (K*G(s))/(1+K*G(s))[/tex]
This transfer function is a ratio between the gain of the controller (K) and the plant’s open-loop transfer function (G). The denominator is the sum of the gain and the plant’s transfer function, which results in the closed-loop feedback loop.
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A 16-inch board is to be cut into three pieces so that the second piece is 3 times as long as the first piece and the third piece is 4 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.
Answer:
Step-by-step explanation:
oi gooot
You have a ruler of length 2 and you choose a place to break it using a uniform probability distribution. Let random variable X represent the length of the left piece of the ruler. X is distributed uniformly in [0, 2]. You take the left piece of the ruler and once again choose a place to break it using a uniform probability distribution. Let random variable Y be the length of the left piece from the second break. Draw a picture of the region in the X-Y plane for which the joint density of X and Y is non-zero. Compute the joint density function for X and Y . (As always, make sure you write a complete expression.) Compute the marginal probability density for Y , fY (y). Compute the conditional probability density of X, conditional on Y = y, fX|Y (x|y). (Make sure you state the values of y for which this exists.)
a) The region in the X-Y plane for which the joint density of X and Y is non-zero is a triangle with vertices at (0,0), (0,2), and (2,2).
b) The joint density function for X and Y is given by: f(x,y) = 1/2 for 0 < x < y < 2.
c) The marginal probability density for Y is given by: fY (y) = ∫ f(x,y) dx = (1/2) y for 0 < y < 2.
d) The conditional probability density of X, conditional on Y = y, is given by: fX|Y (x|y) = f(x,y)/fY (y) = 2 for 0 < x < y < 2.
This only exists for 0 < y < 2.
a) The region in the X-Y plane for which the joint density of X and Y is non-zero is a triangle with vertices at (0,0), (0,2), and (2,2). This is because the lengths of the two pieces of the ruler must be non-negative and must add up to 2.
b) The joint density function for X and Y is given by:
f(x,y) = 1/2 for 0 < x < y < 2.
c) The marginal probability density for Y is given by:
fY (y) = ∫ f(x,y) dx = (1/2) y for 0 < y < 2.
d) The conditional probability density of X, conditional on Y = y, is given by:
fX|Y (x|y) = f(x,y)/fY (y) = 2 for 0 < x < y < 2. This only exists for 0 < y < 2.
Note: The factor of 1/2 in the joint density function accounts for the uniform distribution of the two breaks on the ruler, while the factor of 2 in the conditional density function accounts for the change of variables from the joint density to the conditional density.
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The magnitude and direction of vectors t, u, and v are shown in the table.
Vector Magnitude Direction
t 5 250°
u 6 60°
v 12 330°
What is the direction of t + u + v? Round to the nearest degree.
335°
305°
155°
213°
The direction of t+ u+ v is 155°.
What is a vector?A vector is a quantity that possesses magnitude, direction, and adheres to the law of vector addition.
Given:
The magnitude and direction of vectors t, u, and v are shown in the table.
Vector Magnitude Direction
t 5 250°
u 6 60°
v 12 330°
The coordinates of the resultant vectors:
t + u + v,
= (5 cos250° + 6cos60° + 12cos330°, 5 Sin250° + 6Sin60° + 12Sin330°)
= (11.7, -5.5)
Now, the direction of t+ u+ v = arc tan(-5.5/11.7)
= 155°
Therefore, 155° is the direction.
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Answer:
335°
Step-by-step explanation:
I took the test and got it right :)
Please help me 10 points
Answer: Its 4(x+1)
Step-by-step explanation:
You combine all the x's, creating 4x+4.
In the last answer, it has 4(x+1) which by distributing you should get 4x+4!
suppose that a die is rolled twice. what are the possible values that the following random variables can take
A) The maximum value to appear in the two rolls can take on any value from 2 to 6.
B) The minimum value to appear in the two rolls can take on any value from 1 to 5.
C) The sum of the two rolls can take on any value from 2 to 12.
D) The value of the first roll minus the value of the second roll can take on any value from -5 to 5.
If the die is assumed to be fair, the probabilities associated with the random variables in parts (a) through (d) can be calculated as follows:
A) The probability of the maximum value to appear in the two rolls is 1/6.
B) The probability of the minimum value to appear in the two rolls is 1/6.
C) The probability of the sum of the two rolls is 1/36 for each of the possible sums from 2 to 12.
D) The probability of the value of the first roll minus the value of the second roll is 1/11 for each of the possible values from -5 to 5.
Complete question:
Suppose that a die is rolled twice. What are the possible values that the following random variables can take on (a) the maximum value to appear in the two rolls: (b) the minimum value to appear in the two rolls (c) the sum of the two rolls; (d) the value of the first roll minus the value of the second roll? 4.8. If the die in Problem 4.7 is assumed fair, calculate the probabilities associated with the random variables in parts (a) through (d).
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Find the mean, median, and mode of the set. Round to the tenths place, if needed: 3.1, 4.5, 4.3, 4.5, 8.0, 3.2
The mean, median and the mode of the given sets of data above would be = 3.3, 4.3, and 4.5 respectively.
What is a mode?A mode is the value in a data set that appeared the most when compared with others.
The mode of this data set = 4.5. This is because it appeared twice.
The median of the data set is the value that is at the middle after being arranged.
The median of the data set = 3.1,3.2,4.3,4.5,4.5 = 4.3
The mean of the data set = 3.1+3.2+4.3+4.5+4.5/6
= 19.6/6
= 3.3
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